Developmental and Phenological Modeling of Russian Wheat Aphid (Hemiptera: Aphididae)

We applied 14 insect development models, both deterministic and distributed, to describe Russian wheat aphid, Diuraphis noxia</it> (Mordvilko) (Hemiptera: Aphididae), development and phenology. The Russian wheat aphid developmental data were from a laboratory experiment of 25 combinatorial treatments of five temperatures and five spring barley, Hordeum vulgare</it> L., plant growth stages. The developmental times of 1,800 individual Russian wheat aphids at various stages were recorded in the experiment. We first compared 11 deterministic development models and discussed some problems associated with the fitting of these models. Not all nonlinear models could be fitted to every Russian wheat aphid stage. The results show that Stinner’s model overall best fit Russian wheat aphid developmental rate data, as judged by mean square error (MSE) and successful convergence. However, we observed a seemingly inescapable dilemma: when one introduces more complex nonlinear models to increase the descriptive power of models (with the hope that model parameters have some biological meanings), the more difficult it is to successfully fit the model. Even if the model is fitted successfully, the values of the model parameters may well be beyond biologically meaningful ranges. Furthermore, we believe that a potentially more serious trap associated with complex nonlinear model is the extreme low tolerance of model parameters. Our results show that the extreme low tolerance associated with the parameter estimate may occur even if the MSE of model fitting is very small. The second part of our results presented same-shape distribution models for Russian wheat aphid development. Stinner’s model performed well and successfully fitted all 22 data sets, whereas the Weibull distribution and logistic model only succeeded in 17 and six of 22 data sets, respectively. Finally, Population Model Design System software was used to simulate Russian wheat aphid phenology based on the integration of deterministic nonlinear developmental rate models and same-shape distributions models.